I think about non-Euclidean space sometimes. Hyperbolic space in particular -- space with negative curvature. Parallel lines bend away from each other and are lost in infinity.
I've watched videos and played with math toys. Hypernom is pretty good. (Let it go full-screen, then move around with arrow keys, or touch the screen and use orientation on a mobile device. Or see other links at Henry Segerman's VR page.)
My favorite game to get a feel for hyperbolic space remains HyperRogue. This game has been around for a while (and I've never linked to it? Jeez). Give it a shot if you haven't. The author just added a VR option...
Now, I'm not talking about "wrapped" spaces like Manifold Garden. Those can hurt the head, but they're basically Euclidean -- parallel lines stay parallel. (A portal or two doesn't change the basic metric.) "Nested" spaces are more interesting; that's repeating infinitely at smaller and smaller scales, or larger if you go outwards. (Maquette, or that scene in The Room 4: Old Sins.) Again, nifty! But this post is about space which distorts with every step you take through it.
(HyperRogue is the best-known example, but other games are picking up on the idea. Hyperbolica looks like it could be good.)
When you wander around HyperRogue, you can tell there's more space than there should be. Whatever direction you go, you can get lost in a wilderness. You spot a small island in the distance, but as you approach, you realize its perimeter is a straight line -- there's just as much territory "inside" as "outside". And there are lots of these "islands"!
If this makes no sense, then you didn't give it a try when I told you too. Or just watch the video, okay? It's hard to describe! Which bothers me! I'm a text guy. Can we get this experience of hyperbolic space into a text game? Does that make sense?